Problem 11, Page 303

\[ \mu / n = 1000/100 = 10 hours \]

Problem 14, Page 303

\[ \int_{-\infty}^{\infty} f_X(z + y) f_Y(y) dy\] \[ = \int_{0}^{z} \lambda e^{-\lambda(z+y)} \lambda e^{-\lambda y} dy\] \[ = \int_{0}^{z} \lambda e^{-\lambda(z+y)} \lambda e^{-\lambda y} dy\] \[ = \int_{0}^{z} \lambda^2 e^{-\lambda(z+2y)} dy\] \[ = (1/2) \lambda e^{-\lambda |z|}\]

Problem 1, Page 320

Chebyshev’s Inequalities:

  1. P(|X-10|>=2) <= (100/3) / (2^2) = 8.333

  2. P(|X-10|>=5) <= (100/3) / (5^2) = 1.333

  3. P(|X-10|>=9) <= (100/3) / (9^2) = 0.412

  4. P(|X-10|>=20) <= (100/3) / (20^2) = 0.083